l=1 electrostatic instability induced by electron-neutral collisions in a nonneutral electron plasma interacting with background neutral gas

This paper investigates theoretically the electrostatic stability properties of a nonneutral electron plasma interacting with background neutral gas through elastic collisions with constant collision frequency νen. The model treats the electrons as a strongly magnetized fluid (ωpe2/ωce2<1) immersed in a uniform magnetic field B0ez, and assumes small-amplitude perturbations with azimuthal mode number l=1 and negligible axial variation (∂/∂z=0). The analysis also assumes weak electron collisions with νen/ωce=ε<1, and that the process of heat conduction is sufficiently fast that the electrons have relaxed through electron-electron collisions to a quasiequilibrium state with scalar pressure P(r,θ,t)=n(r,θ,t)T, and isothermal temperature T. Assuming that perturbed quantities vary with time according to exp(-iωt), the detailed stability analysis carried out to first order in νen/ωce<1 shows that the real oscillation frequency and growth rate for the l=1 diocotron mode are given, respectively, by the simple expressions Reω=ω0 and Imω=(νen/ωce)ω0. Here, ω0=Nec/r2wB0, where rw is the perfectly conducting wall radius, and N=∫d2xn is the number of electrons per unit axial length. This analysis suggests that a measurement of the oscillation frequency and growth rate for the l=1 diocotron mode can be used to infer νen, and thereby serve as a sensor for the background neutral pressure. copyright 1996 American Institute of Physics